The convergent and discrete maximum principle of finite element methods for solving the convection-diffusion-reaction problem

Abstract EN

In this paper, we describe several finite element methods for solving the Convection-Diffusion-Reaction problem (CDR) and study two important properties for the approximate solution, the convergent and the discrete maximum principle.

For convergence we considered two cases, semi-discrete and discrete methods, for semi-discrete, we prove that all scheme are converge with (hr), where h refers to the discretization parameter, and s is a degree of polynomials of finite element space and for discrete we proved that all schemes converge with (hr).

Finally, the discrete maximum principle and L-stable are proved.